Lower and upper bounds for the provability of Herbrand consistency in weak arithmetics

Zofia Adamowicz, and Konrad Zdanowski. "Lower and upper bounds for the provability of Herbrand consistency in weak arithmetics." Fundamenta Mathematicae 212.3 (2011): 191-216. <http://eudml.org/doc/283125>.

@article{ZofiaAdamowicz2011,
abstract = {We prove that for i ≥ 1, the arithmetic $IΔ₀ + Ω_i$ does not prove a variant of its own Herbrand consistency restricted to the terms of depth in $(1+ε)log^\{i+2\}$, where ε is an arbitrarily small constant greater than zero. On the other hand, the provability holds for the set of terms of depths in $log^\{i+3\}$.},
author = {Zofia Adamowicz, Konrad Zdanowski},
journal = {Fundamenta Mathematicae},
keywords = {Herbrand consistency; unprovability; weak arithmetics},
language = {eng},
number = {3},
pages = {191-216},
title = {Lower and upper bounds for the provability of Herbrand consistency in weak arithmetics},
url = {http://eudml.org/doc/283125},
volume = {212},
year = {2011},
}

TY - JOUR
AU - Zofia Adamowicz
AU - Konrad Zdanowski
TI - Lower and upper bounds for the provability of Herbrand consistency in weak arithmetics
JO - Fundamenta Mathematicae
PY - 2011
VL - 212
IS - 3
SP - 191
EP - 216
AB - We prove that for i ≥ 1, the arithmetic $IΔ₀ + Ω_i$ does not prove a variant of its own Herbrand consistency restricted to the terms of depth in $(1+ε)log^{i+2}$, where ε is an arbitrarily small constant greater than zero. On the other hand, the provability holds for the set of terms of depths in $log^{i+3}$.
LA - eng
KW - Herbrand consistency; unprovability; weak arithmetics
UR - http://eudml.org/doc/283125
ER -